拆、猜、看--尋找正方體十一個展開圖策略

Abstract

本研究是一個「尋找正方體展開圖課程」的前導研究，旨在透過個案觀察，以期能發現學生在尋找展開圖時可能遭遇的困難或可能有的解題策略，用以提供將來發展以「學生中心」的正方體展開圖的課程時更完整的設計。個案是一名國中七年級的學生，數學成績屬於班上中上，也就是前10%左右。最後發現，尋找正方體展開圖的策略恰為拆、猜、看三種策略，也就是可以直接拆開一個盒子來找展開圖、或是先猜猜看可能展開圖的樣子，再試試看能不能拼成一個盒子，或是拆開盒子的上方正方形來觀察可能拆出的樣貌，再做展開圖。這些策略可供想要發展以學生中心課程設計的教師做課程設計之參考。

This study is a pilot study for developing the curriculum about "looking for the eleven developments of a cube". For the purpose of finding out the difficulties and strategies when looking for the eleven development of cube, and in order to develop the more complete design curriculum of "looking for the eleven developments of a cube" in the "student-centered teaching and learning" way, we plan through the case-study. The student participate in this study is a seven grades student, and math scores is upper average of the class, about top 10%. Finally, we found out the three strategies of this student when she finishes looking for the eleven developments of a cube, three strategies are split, guess and see. You can split a cube to get a development, and you also can guess what development may splice it into a cube then splice it, and you also can split the cover of a cube to see how to split the cube into different development. These strategies are available for reference to the teachers who want to develop a "student-centered teaching and learning" course about "looking for the eleven developments of a cube".